Epsilon Open Archive

Abstract

In Politis and Romano (1993), different block resampling estimators of variance of general linear statistics, e.g. a sample mean, were proposed under the assumption of stationarity. In the present paper such estimators of variance of sample means, computed from nonstationary spatially indexed data {Xi : i E A}, where A is a finite subset of the integer lattice Z2, are studied.
Consistency of estimators of variance will be shown for the following kind of data: Observations taken from different lattice points are allowed to come from different distributions, and the dependence structure is allowed to differ over the lattice. We assume that all observed values are from distributions with the same expected value, or with expected values that decompose additively into
directional components. Furthermore, it will be assumed that observations separated by a certain distance are independent.